The goal-shy Glovers have found the net only six times in a dozen matches and have not secured a win since their opening day success at Millwall.
Johnson admitted his team were still learning at this level, but backed them to soon find their feet and push up the division.
He said: "I don't think either side deserved to lose. It was a cagey game, but when you come up against a team like Brighton, who were only one or two games away from the Premier League last year, then you mustn't be too disappointed with a point.
"We may have gone bottom of the league, but we're gaining experience against these types of teams who keep the ball and are clever.
"Our league is a mini-league with the bottom six or seven teams and I'm sure Brighton won't be in there.
"We created some chances, but they were not unbelievable chances. You have to concentrate against teams like Brighton. They keep the ball and it's really hard to get it back.
"I think we gave the ball back to them too easily and that's what we have to be better at. The boys gave it everything and we had the opportunities to win the game.
"It's a bit early to be worrying about league position, but at the same time we've got to gradually push our way out of the bottom three."
Brighton assistant head coach Nathan Jones admitted the Seagulls lacked a "killer edge" in the final third at Huish Park, but claimed new signing Leroy Lita would prove a hit.
He said: "We were a little disappointed as we felt we did enough to win the game. We had enough possession and enough chances.
"I think anyone who has watched us for the last two months have seen we create enough chances, but we've got players like Craig Mackail-Smith and Will Hoskins out injured. I think we're missing that goalscorer to win us games.
"We've signed Leroy and hopefully we can bring another in, but it's taking too long to do that.
"I thought Leroy looked lively. He hasn't played much football lately and he's not ready for 90 minutes yet, and that's the trouble we have.
"He brings potency, he knows the role and everywhere he has gone he has scored goals. He's sharp and powerful, and hopefully will score goals for us.
"The pleasing thing today was our performance. We worked hard and kept a clean sheet, but it's just that killer edge that let us down."